At the centre of the row is the "Cuban Liberty and Democratic Solidarity (Libertad) Act" of 1995, introduced by Jesse Helms, the virulently conservative chairman of the Senate Foreign Relations Committee.
It would, among other things, punish European-based subsidiaries of US corporations for dealings with Cuba, ban European sugar companies from business here if they import Cuban sugar, and deny US visas to executives of companies doing business there.
In letters to the House Speaker, Newt Gingrich, and Bob Dole, the Senate majority leader, the EU warns the bill infringes the sovereignty of its member states, and could have "grave and damaging" effects on Washington's ties with Europe.
Separately, Sir Leon Brittan, vice-president of the European Commission, has written to the Secretary of State, Warren Christopher, saying the measure violates Gatt rules and could cause "legal chaos". It also will not help progress towards a "peaceful and orderly" transition to democracy in Cuba, he said.
America's unremitting vindictiveness towards the ageing leader of a virtually bankrupt Caribbean island never fails to baffle outsiders, as well as many Cuba specialists who point out that punitive policies may only strengthen Mr Castro.
Such considerations, however, pale beside domestic politics, especially when a presidential election is barely 18 months away. The prize is the fiercely anti-Castro Cuban-American vote, believed to hold the key to success in Florida.
The White House has thus far said merely that it would seek to knock some of the rougher edges off the bill. Mr Clinton has no realistic hope of carrying Florida in 1996 but wants to protect Governor Lawton Chiles, his party's sole governor in the eight largest states.
Cuba yesterday condemned the US for expelling two of its UN diplomats over an alleged assault on New York City policemen last August.
nVowing to reverse America's "cultural meltdown and moral decline", Congressman Robert Dornan, 62, of California entered the contest for the Republican presidential nomination yesterday. He has no chance of winning but could steal votes from other conservatives, such as Senator Phil Gramm of Texas.